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The electric field distribution in electronic devices, particularly in the organic devices, was visualized by the optical second harmonic generation (SHG) imaging technique on the basis of electric field induced SHG (EFISHG). Two-dimensional SHG images from organic field effect transistor using pentacene were taken with a cooled CCD camera, and the SHG images showed the electric field was successfully visualized with a resolution of 1 µm. The SHG imaging method provides us a novel technique for visualizing the electric field distribution in actual devices under device operation.
©2007 Optical Society of America
1. Introduction
The basic equation that expresses a current flowing in materials, J=enµE, implies that the electric field distribution, E, in electronic devices plays a significant role in determining the device characteristics, where e, n and µ represent fundamental charge, carrier density and mobility, respectively. Also, the electric field in materials dominates a variety of carrier transport phenomena such as space charge limited current (SCLC), where zero electric field at an injection point is a-priori boundary condition for the SCLC [1]. The development of the scanning probe technique enables us to evaluate the potential distribution in devices with high resolution [2, 3, 4]. For inorganic semiconductor devices, such as silicon-based transistors, thermal equilibrium of carriers is assumed to be established in the devices. Under the establishment of the thermal equilibrium, carrier distribution is ruled by Fermi-Dirac Statistics, and its density is given as a function of electrostatic potential; thus we perceive the importance for the direct evaluation of a potential distribution in inorganic semiconductor devices. On the other hand, direct evaluation of the electric field distribution rather than the potential distribution is an essential issue for low conductive materials such as organic materials with a large energy gap. This is because the thermal equilibrium is not completely established in the devices composed of such low conductive materials, but the current equation, J=enµE, is always valid. In this sense, it is worthwhile developing a technique, which can evaluate directly an electric field distribution in devices.
Electric field induced second harmonic generation (EFISHG) is one of the third-order nonlinear optical processes, and it generates second harmonic light of the fundamental light in the presence of a dc electric field. For the EFISHG process, applied electric field induces the effective polarization in materials. In a typical EFISHG experiment, the molecules with nonzero dipole moments are dissolved in a solvent and the dc electric field is applied to estimate the molecular hyperpolarizability [5, 6]. Also, SH activation in poled polymers is well known, where the dipolar side chains of polymers align along the electric field. Therefore, orientational polarization contributes to the SHG in the case of poled polymer. For the symmetric molecules such as pentacene and phthalocyanine, there is no orientational polarization induced by the external electric field. In such cases, the distribution of delocalized π -electron is distorted by the external field and effective polarization is induced, i.e., electronic polarization. According to the symmetric consideration of the susceptibility tensor, the SHG signal vanishes from centrosymmetric media under the electric dipole approximation. However, the external electric field breaks such centrosymmetry, and we can observe the SHG signal from the centrosymmetric media.
For the EFISHG, the SHG intensity is proportional to the external field as,
where χ(3)(-2ω;0,ω,ω) represents a third order nonlinear optical (NLO) susceptibility for the EFISHG process, and E(0) and E(ω) represent the static electric field and electric field of light, respectively. Thus the information about electric field in materials can be obtained by the EFISHG measurement, and the EFISHG was effectively employed as a probe of the electric field near a Au-silicon Schottky interface [7]. We have also proposed methods for evaluating the electric field distribution in organic devices on the basis of the scanning EFISHG measurements [8]. As mentioned in our previous paper, to obtain the electric field distribution from the SHG intensity distribution requires a deconvolution process taking into consideration the beam profile of fundamental laser. Such deconvolution is, in general, a laborious task, because a beam profile and the SHG intensity profile are not expressed as simple mathematical functions, and the evaluated electric field from a scanning measurement sometimes loses accuracy, e.g. spatial resolution. In this paper, we introduce an SHG imaging technique for visualizing the in-plane distribution of the electric field in the organic devices. The evaluation of the electric field distribution from SHG images does not require the complicated deconvolution process, and the spatial resolution is significantly improved. Moreover, omission of the scanning process results in the reduction of the measurement time.
2. Experiment
Samples used in the experiments were top-contact field effect transistor (FET) structure. Heavily-doped Si wafers were used as the base substrate, and they were covered with a 500 nm thick silicon dioxide (SiO2) insulating layer. The material for the organic semiconductor layer was pentacene (C22H14) purchased from Tokyo Chemical Industry Co., Ltd., and was used as received. Recently, pentacene is one of the standard materials for preparing organic FET (OFET) devices [9, 10, 11]. The pentacene layer, approximately 100 nm thick, was deposited on a SiO2 surface. The process pressure during deposition of pentacene was kept at less than 1×10-4 Pa, and the deposition rate was controlled at approximately 3 nm/min. After the deposition of pentacene, top-Au electrodes (source and drain electrodes) with a thickness of 100 nm were deposited on the pentacene surface. The channel length (L) and width (W) were 50 µm and 3 mm, respectively. For the FET structure, the Si substrate was used as the gate electrode. Figure 1(a) represents the schematic images of the sample structure and electrical connection.
Fig. 1. (a) Schematic images of the sample strucrure and electrical connection. (b) Optical setup for the SHG imaging.
The light source for the SHG measurement was an optical parametric oscillator (OPO: Con- tinuum Surelite OPO), pumped by a third-harmonic light of Q-switched Nd-YAG laser (Continuum: SureliteII-10). The use of an appropriate wavelength is important to observe the SHG signal from pentacene effectively, because the SHG intensity strongly depends on the fundamental wavelength. For the EFISHG process, resonance enhancement occurs at both forbidden and allowed excited states. In our previous paper [12], we discussed the EFISHG spectrum of vacuum deposited pentacene films. As a result, the EFISHG peaks were located at 1120 nm and 1320 nm, and a fundamental wavelength was fixed at 1120 nm in this study. Fundamental light from the OPO passed through a prism polarizer, long-pass filters and a beam expander (see Fig. 1(b)). Then it was focused on the channel region of the FET with normal incidence, using a long working distance objective lens (Mitsutoyo: M Plan Apo SL20×, NA=0.28, W.D.=20.5 mm). SH light generated from the FET was filtered by a fundamental-cut filter and an interference filter to remove fundamental and other unnecessary light. Finally, SH light was detected by a cooled CCD camera (Andor technology: BV420-DR). In this configuration, the polarization direction of the light was chosen in the direction corresponding to the channel direction (source-drain direction).
Note that, there were some differences in the optical setup between scanning measurements and SHG imaging. One is the detector for the SHG observation. For the scanning measurement, a photomultiplier tube was used to detect the SHG light, whereas a cooled CCD camera was used to take an SHG image. Another difference was the spot size of the fundamental light. To obtain the SHG intensity distribution on the basis of the scanning measurement, we needed to reduce the spot size because the spatial resolution depends on the spot size. On the other hand, the fundamental light should irradiate a large area of the channel region for SHG imaging. Thus we used a beam expander for the SHG imaging.
All measurements were performed in laboratory ambient atmosphere. To avoid unexpected injection of carriers from the electrode, the pentacene FET was operated by pulsed voltage. Under the negative bias application to the drain electrode, electron injection is difficult because of the large injection barrier for electron from the Au electrode to pentacene (see Fig. 1(a)). Pulsed voltage was applied to the drain electrode using a function generator (NF Corp.: WF1974) amplified by a high-speed bipolar amplifier (NF Corp.: HSA 4101), and the source and gate electrodes were connected to the ground. The pulse width, repetition rate and amplitude applied to the FET were 20 µs, 10 Hz and 70 V, respectively. The external Q-switch trigger of the Nd-YAG laser was supplied simultaneously from the function generator. The time delay between the pulse voltage applied to the FET and the Q-switch trigger was controlled precisely by the function generator, and was fixed at 100 ns.
3. Scanning SHG measurement
Because EFISHG is a third-order NLO process, susceptibility tensor does not vanish in the centrosymmetric media. Since the SHG intensity is related to the internal electric field in materials as expressed in Eq.(1), the electric field distribution can be evaluated using SHG intensity distribution. To obtain SHG intensity distribution in OFET, microscopic SHG measurement was employed [8]. Here, we introduce briefly scanning SHG measurement for evaluating the electric field distribution. For the microscopic SHG measurement, fundamental light is focused onto the sample surface using microscopic objectives, and the SHG signals from this spot are acquired. The sample stage is moved sequentially to change the spot position, and the SHG intensity was acquired at each position. Accordingly, we can obtain the SHG intensity distribution. SHG intensity at position x, I2ω (x), is expressed by a convolution of the beam profile of the fundamental laser and the actual electric field distribution as,
where E(ξ) and Iω(ξ) represent the electric field distribution and the intensity profile of the fundamental laser, respectively. The boundary conditions for the calculation are ∫L0E(ξ)dξ=Vds and E(ξ)=0(ξ<0,ξ>L). Nevertheless, the SHG distribution strongly depends on the intensity profile of the fundamental laser.
Fig. 2. SHG profiles along the pentacene FET channel obtained using (a) 20× and (b) 50× objective lens. Two-dimensional intensity distrubution of fundamental light at a focal point using (c) 20× and (d) 50× objectives.
Figures 2(a) and 2(b), respectively, represent the SHG profiles along the pentacene FET channel obtained using the 20× and 50× objective lenses, together with the in-plane electric field distribution in the pentacene layer calculated based on a finite element method. Figures 2(c) and 2(d) show the two-dimensional intensity distribution of the fundamental light at a focal point using the 20× and 50× objectives, respectively. In these measurements, SHG signals were acquired at an interval of 5 µm along the channel, and the region from 20 µm to 70 µm corresponding to the channel (L=50 µm). Open circles and solid line represent the SHG intensity at each spot position and electric field distribution. Remarkable SHG signals were observed on the drain side as shown in the figure. High electric fields between drain and gate electrodes also produced a large in-plane component of the electric field around the drain electrode due to the edge effect. Such large in-plane component of the static field effectively contributes to the SHG because of the normal incidence of the fundamental light. For both figures, the SHG profiles are widely distributed compared with the electric field distribution. Moreover, comparing the SHG distribution obtained using the 20× objective with that obtained using 50× objective, large magnification lens clearly causes the sharp SHG distribution.
4. SHG imaging using cooled CCD
As mentioned above, the SHG intensity profile obtained on the basis of a scanning measurement does not display an actual spread of SHG emission in the channel. Direct observation of the SHG image in the channel can show a more realistic distribution of the SHG emission within the limits of the system resolution. Figure 3(a) shows the SHG image from the channel of pentacene FET under the application of negative pulse. As shown in the figure, strong SHG emission was observed at an edge of drain electrode. As well as the scanning SHG measurement where a remarkable SHG peak was observed on the drain side, high electric fields between the drain and gate electrodes produced a large in-plane component of the electric field, and it activated the SHG at the drain edge. It is noteworthy that the width of the SHG emission in the channel clearly decreases compared with a distribution obtained on the basis of a scanning measurement.
Fig. 3. (a) SHG image from the channel of pentacene FET under the application of negative pulse. Channel region lies between two gold electrodes, and edges of the electrode are indicated by dashed lines. SHG emission was observed at the edge of the drain electrode. (b) Microscopic image of the channel between two electrodes. This picture was taken under the illumination of visible light.
Figure 4 shows the line scan of the SHG intensity profile across the channel (represented as open squares and filled diamonds) and the in-plane component of the in-plane electric field distribution (solid line) in the pentacene layer. Open squares and filled diamonds, respectively, represent the SHG intensity profile at line scan A and B as shown in Fig. 3. The electric field distribution represented here is similar to that represented in Fig. 2, though this image is magnified. The edge of the electrode is located at a position of 70 µm in these figures. As shown, it is found that the SHG intensity profile is quite sharp compared with the result of the scanning measurement (see Fig. 2). The sharpness of emission is quantitatively estimated using full width at half maximum (FWHM) values of the profile. FWHM values of SHG profile and the electric field distribution are evaluated as 0.9 µm and 0.7 µm, respectively. Note that FWHM values of the SHG profile obtained based on the scanning measurement depended on the magnification of the objective lens and was approximately 15 µm for 20× objective.
For the electric field calculation, there were no excess charges in the device, and only the electrode configuration and potential were taken into account. In such case, Laplacian electric field is formed in the device. Laplacian field is the electric field in an insulator caused by the electrodes in the absence of any charges between the electrodes. Under the negative bias, carrier injection from the electrode into pentacene is prohibited because the injection barrier for electrons at the pentacene/Au interface is quite high, i.e., energy difference between the lowest unoccupied molecular orbital (LUMO) of pentacene and the work function of Au electrode was evaluated as 2.7 eV [13]. Thus the strong electric field around the edge of the electrode was maintained during bias application, and the SHG emission concentrated around the edge of the drain electrode as shown. In other words, the sharp emission of the SHG at the edge of the electrode indicated that the SHG imaging technique successfully visualized the electric field in the device with a spatial resolution of approximately 1 µm. Futhermore, it should be noted that the intensity correction of the SHG images based on the spatial distribution of fundamental light can improve the accuracy of electric field evaluation.
Fig. 4. Top figure represents the in-plane component of the in-plane electric field distribution in pentacene layer. Bottom one shows the line scan of the SHG intensity profile across the channel. Open squares and filled diamonds, respectively, represent SHG intensity profile at line scan A and B as shown in Fig. 3.
The tensor origin of the EFISHG from the pentacene FET should be briefly discussed. According to AFM images of our samples, vacuum evaporated pentacene films were composed of many small grains with a size of less than 400 nm (not shown). Thus we can reasonably consider the C∞v symmetry for a pentacene layer. Under the C∞v symmetry, there are 7 independent components of the NLO susceptibility for the EFISHG process. Since the x-directional component of the electric field composed a fundamental light with a normal incidence, only the χxxxx component contributes to the SHG signal. This indicates that x-component of the internal static electric field can be selectively evaluated.
The electronic devices using organic materials such as OFET and organic light emitting diode have attracted much research attention due to their potential for the practical application [14]. In particular, recent focus in the field of the organic electronics is to employ an easy process such as ink-jet printing method for fabricating devices [15]. π -Conjugated polymers is the strong candidate for the appropriate materials using in such so-called wet-process, and the development of well-modified π -conjugated polymers with high mobilities becomes important. Nevertheless, the sensitivity of the SHG imaging method depends on the third-order NLO susceptibility, χ (3). π -Conjugated polymers show, in general, large χ (3) values because of the presence of extensively delocalized π -electrons. In this sense, the SHG imaging method for evaluating the electric field distribution also contributes to the development of polymer electronics.
5. Conclusion
Electric field distribution in electronic devices, particularly in organic devices, was successfully visualized by the optical SHG imaging technique on the basis of electric field induced SHG. Two-dimensional SHG images from OFET using pentacene were taken with a cooled CCD, and the SHG images showing the electric field was successfully evaluated with a resolution of 1 µm.
Acknowledgement
This work is support by the Grants-in-Aid for Scientific Research (Grant No.18686029, 19206034) from Ministry of Education, Culture, Sports, Science and Technology and The New Energy and Industrial Technology Development Organization (NEDO).
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